Immigration Policy in a Time of Secular Stagnation Jorge Barro Rice University Baker Institute of Public Policy September 21, 2019
Overview ◮ Significant demographic transition in the US over last century ◮ Macroeconomic implications - Secular Stagnation ◮ Fiscal consequences - Social Security, Government Debt, Monetary Policy ◮ Focus on immigration as an economic policy instrument
Empirical Overview Value ’75-’85 ’08-’18 RGDP Growth 3.2% 1.5% Investment Growth 5.0% 2.7% 251% 1 Net Worth/GDP 372% Interest Rates 2.91% 0.86% 1 1987 value
Mechanism ◮ Rise in life expectancy, decline in birth rate ◮ Relative rise in share of households nearer to peak of life-cycle wealth ◮ Rise in wealth relative to output ◮ Declining interest rates
Related Literature ◮ Eggertsson, Lancastre, Summers (2018) ◮ Ariby, Geppert, Ludwig (2017) ◮ Storesletten (2000)
Questions ◮ To what extent can immigration policy resolve demographic imbalances? ◮ How much can skilled immigration improve economic growth? ◮ How much immigration would it take to reach 4% growth? ◮ How can immigration impact the fiscal outlook?
Goals ◮ Present a model accounting for demographics (age, education) ◮ Explain macroeconomic trends since 1980’s ◮ Evaluate counterfactual immigration policies
Model Overview ◮ Standard OLG, production economy ◮ Two types - high/low productivity ◮ Linear income tax per type ◮ Cohort-dependent birth rates and survival rates ◮ Historical immigration rates by education
Agent Optimization ◮ Agent of cohort j with education e at time t solves: j , t (1 − n j , t ) 1 − γ � 1 − σ � c γ V j , t ( a j , t ) = max + s j , t β V j , t +1 ( a j , t +1 ) 1 − σ c j , t , n j , t , a j , t +1 (1) s.t. c j , t = w t ǫ e z t − j +1 n j , t + (1 + r t ) a j , t − a j , t +1 − φ e ( · ) (2) φ e ( · ) = τ e ( w t ǫ e z t − j +1 n j , t + r t a j , t ) (3) and a j , j + J +1 ≥ 0, (4)
Firm Optimization ◮ Firms solve: t ( A t L t ) 1 − α − ( r t + δ ) K t − w t L t max K t , L t K α (5) ◮ Optimality conditions: � K t � α − 1 r t = α − δ (6) A t L t � K t � α w t = (1 − α ) . (7) A t L t
Government ◮ Aggregate tax revenue: t − J +1 � � µ e Φ t = j , t φ e ( · ). (8) j = t e ∈{ h , l } ◮ Government budget constraint: G t = Φ t + B t , (9)
Equilibrium Dynamic general equilibrium: prices { w t , r t } and quantities � � c ∗ j , t , n ∗ j , t , a ∗ such that: j , t +1 1. Given prices and government policy, agents choices satisfy Equation 1 - Equation 4, 2. Prices are determined in competitive markets according to Equation 6 and Equation 7, 3. Markets clear: ◮ K t = � t − J +1 e ∈{ h , l } µ e � j , t a j , t +1 j = t ◮ L t = � t − J +1 � e ∈{ h , l } µ e j , t ǫ e z t − j +1 n j , t j = t ◮ Y t = C t + K t +1 − (1 − δ ) K t + G t 4. Government budget constraint (9) is satisfied. 5. Accidental bequests received by the government are determined according to t − J +1 � � (1 − s j , t ) µ e B t = j , t a j , t +1 . (10) j = t e ∈{ h , l }
Equilibrium Error 10 -15 Normalized Resource Error 5 0 -5 0 100 200 300 400 500 600 Periods
Population Dynamics ◮ Natives: µ e j , t +1 = s j , t µ e (11) j , t ◮ Immigrants: µ e µ e j , t + m e ˜ j , t +1 = s j , t ˜ (12) j , t +1 ◮ Population: t − J +1 � � � µ e µ e � M t = j , t + ˜ (13) j , t j = t e ∈{ h , l }
Population Dynamics ◮ Native newborns: � µ e t +1 , t +1 = ζ t M t (14) e ∈{ h , l } - ζ t is the birth rate at time t . - Education shares determined by education rates by cohort.
Population Dynamics ◮ Immigrants: � m e j , t = ψ t λ j , t M t (15) e ∈{ h , l } - ψ t is the immigration rate at time t . - Education shares determined by immigrant education rates by year.
Population Dynamics ◮ Define relative population at time t as: t − J +1 � � µ e µ e � j , t + ˜ e ∈{ h , l } j , t (16) M t j = t ◮ Population is relatively stable if ∀ ε > 0 ∃ t ( ε ) > 0 such that t > t ( ε ) ⇒ � t − J +1 ( t +1) − J +1 � � � � � µ e µ e µ e µ e � � � j , t + ˜ j , t + ˜ � e ∈{ h , l } e ∈{ h , l } � j , t j , t � max � � < ε − � � M t M t � � j = t j = t +1 � � (17)
Computing Population Dynamics 1. Using earliest available data, find relatively stable population. 2. Allow demographics to change over the transition. 3. Iterate until new relatively stable population (and stable prices) reached.
Parameters Parameter Symbol Value Coefficient of Relative Risk Aversion 3 σ Consumption Share of Utility γ 0.65 Discount Factor β 1.025 Maximum Age 120 J Capital Share α 0.36 Depreciation Rate δ 0.085 Labor Productivity Growth Rate 0.015 g Education Premium ǫ e 170% Tax Rate - college not attained τ l 6.2% Tax Rate - college attained 12.1% τ h
Implementing Demographics ◮ Total Change horizon: 1900-2095 ◮ Assume initial value is true dating back to 1900 ◮ Allow historical values to change over transition ◮ Integrate available projections (e.g., birth rates from Census Bureau) ◮ Extrapolate until 2095
Assumptions ◮ Age distribution of entrants equals cross sectional age distribution in 2017. ◮ Birth rate per year is common to all types. ◮ Children of immigrants draw from native college attainment distribution. ◮ Capital of immigrants is the same as natives, per type.
Birth Rates 30 Historical Births/Thousand Projected 20 Extrapolated 10 0 1920 1940 1960 1980 2000 2020 2040 2060 2080 Year
Immigration Rates New Immigrants/Thousand 4 Historical Projected 3 Extrapolated 2 1 0 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 Year
Education Rates: Natives 0.6 Historical College Share Extrapolated 0.4 0.2 0 1920 1940 1960 1980 2000 2020 2040 2060 2080 Year
Education Rates: Immigrants Historical 0.4 College Share Extrapolated 0.3 0.2 0.1 0 1960 1980 2000 2020 2040 2060 2080 Year
Dependency Ratio 0.4 Dependency Ratio 0.3 0.2 0.1 0 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Year
Computing Equilibrium Path ◮ Value function iteration + iterating over K/L ratio ◮ Problem: Don’t want to shock the economy with changing demographics. ◮ Solution: Add more initial periods until economy is “stationary” over the first N periods.
Baseline Economy: Economic Growth 6 Model RGDP 4 2 0 -2 1970 1980 1990 2000 2010 2020
Baseline Economy: Economic Growth 3.5 3.5 Model 3 3 Data Model Data 2.5 2.5 2 2 1.5 1.5 1970 1980 1990 2000 2010 2020 Year
Baseline Economy: Investment Growth 5 4 Model Data 3.5 4 Model Data 3 3 2.5 2 2 1970 1980 1990 2000 2010 2020 Year
Baseline Economy: Capital-to-Output 3.4 4 Model Data 3.2 3.5 Model Data 3 3 2.5 2.8 1970 1980 1990 2000 2010 2020 Year
Baseline Economy: Real Interest Rates 4 4 Model Data 3 3.5 Model Data 2 3 1 2.5 2 0 1970 1980 1990 2000 2010 2020 Year
Baseline Projection: Economic Growth 3.5 3 2.5 2 1990 2000 2010 2020 2030 2040 2050 Year 2 2 LR: Population Growth = 0, Econ Growth Rate = g
Baseline Projection: Investment Growth 4 3.5 3 2.5 2 1990 2000 2010 2020 2030 2040 2050 Year
Baseline Projection: Capital-to-Output 3.6 3.4 3.2 3 1990 2000 2010 2020 2030 2040 2050 Year
Baseline Projection: Real Interest Rates 4 3 2 1 1990 2000 2010 2020 2030 2040 2050 Year
Counterfactual #1 ◮ Increase the immigration rate by 4 × baseline ◮ Mathematically: � m e j , t +1 = 4 ψ t λ j , t M t (18) e ∈{ h , l }
Counterfactual #1: Economic Growth 4 3.5 3 2.5 Baseline Counterfactual 2 1990 2000 2010 2020 2030 2040 2050 Year 3 3 LR: Population Growth = 1.15%, Econ Growth Rate = 2.65%
Counterfactual #1: Investment Growth 15 Baseline Counterfactual 10 5 0 1990 2000 2010 2020 2030 2040 2050 Year
Counterfactual #1: Capital-to-Output 3.6 Baseline Counterfactual 3.4 3.2 3 1990 2000 2010 2020 2030 2040 2050 Year
Counterfactual #1: Real Interest Rates 4 Baseline Counterfactual 3 2 1 1990 2000 2010 2020 2030 2040 2050 Year
Counterfactual #1: Dependency Ratio Dependency Ratio Baseline 0.4 Counterfactual 0.3 0.2 0.1 0 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 Year
Counterfactual #1: Taxes-to-Output 4 vs Baseline 3 2 1 % 0 1990 2000 2010 2020 2030 2040 2050 Year
Counterfactual #2 ◮ Permanently increase college requirement to 100% of immigrants ◮ Gives an upper bound of skill requirement effect
Counterfactual #2: College Share 0.6 Baseline College Share Counterfactual 0.4 0.2 0 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 Year
Counterfactual #2: Economic Growth 3.5 Baseline Counterfactual 3 2.5 2 1990 2000 2010 2020 2030 2040 2050 Year
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